EMTH210-20S1 (C) Semester One 2020

# Engineering Mathematics 2

15 points

Details:
 Start Date: Monday, 17 February 2020 End Date: Sunday, 21 June 2020
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 28 February 2020
• Without academic penalty (including no fee refund): Friday, 29 May 2020

## Description

This course covers material in multivariable integral and differential calculus, linear algebra and statistics which is applicable to the engineering professions.

Mathematics underpins almost every aspect of modern engineering. This is reflected by the fact that all first professional year students must take EMTH210. With the centrality of this course to your professional development in mind, considerable effort has gone into selecting mathematical and statistical topics which will provide the groundwork for you to appropriately mathematise your engineering work. Throughout the course, your lecturers will also endeavour to relate the rigour of the mathematics to the practicality of the situations in which it will be applied, as we concentrate on your ability to apply the techniques to realistic situations.

The following topics will be covered, subject to the time available:
• Partial differentiation, chain rule, gradient, directional derivatives, tangent planes, Jacobian, differentials, line integrals, divergence and curl, extreme values and Lagrange multipliers.
• Second order linear differential equations and their applications.
• Fourier series.
• Double and triple integrals: elements of area, change of order of integration, polar coordinates, volume elements, cylindrical and spherical coordinates.
• Eigenvalues and eigenvectors and their applications.
• Laplace transforms.
• Statistics: approximating expectations, characteristic functions, random vectors (joint distributions, marginal distributions, expectations, independence, covariance), linking data to probability models (sample mean and variance, order statistics and the empirical distribution function, convergence of random variables, law of large numbers and point estimation, the central limit theorem, error bounds and confidence intervals, sample size calculations, likelihood).

## Learning Outcomes

• A student achieving total mastery of this course will be able to:
• Show proficiency in multivariable calculus, including partial differentiation, implicit partial differentiation, the multidimensional chain rule, gradient, directional derivative, tangent planes, Jacobians, differentials, line integrals (exact and inexact), divergence, curl, and Lagrange multipliers.
• Solve homogeneous constant coefficient ODEs and also inhomogeneous constant coefficient ODEs using undetermined coefficients.   This includes ODEs of order other than two.
• Solve elementary second order boundary value problems, and appreciate some applications of BVPs in engineering.
• Calculate real Fourier series of arbitrary period, and employ them to solve ODEs with periodic driving functions.  The student will also be knowledgeable of concepts such as harmonics and Gibbs phenomenon in Fourier series analysis.
• Integrate in multiple dimensions using Cartesian, polar and spherical polar coordinate systems.
• Calculate the eigenpairs of matrices.
• Familiar with orthogonal decomposition, and use it to find the principal axes of an ellipse.
• Proficient in the solution of systems of first and second order ODEs via eigenvalues and eigenvectors, and familiar with the implications defective matrices in such situations.
• Apply Laplace transforms to differential and some integral equations, including those with piecewise functions via the Heaviside step function.
• Approximate expectations.
• Work with random vectors, joint and marginal distributions, independence and covariance.
• Link data to probability models, sample mean, variance, order statistics, and the empirical distribution function.
• Be familiar with convergence of random variables, the law of large numbers, point estimation, the central limit theorem, likelihood, error bounds, and confidence intervals.
• Do sample size calculations.

## Pre-requisites

Subject to approval of the Dean of Engineering and Forestry

## Restrictions

EMTH202, EMTH204, MATH201, MATH261, MATH262, MATH264

## Timetable 2020

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Monday 08:00 - 09:00 C1 Lecture Theatre (17/2-16/3)- (23/3, 20/4)Online Delivery (4/5-25/5) 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May 02 Monday 12:00 - 13:00 C1 Lecture Theatre (17/2-16/3)- (23/3, 20/4)Online Delivery (4/5-25/5) 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May Lecture B 01 Tuesday 09:00 - 10:00 C1 Lecture Theatre (18/2-17/3)- (24/3, 21/4)Online Delivery (28/4-26/5) 17 Feb - 29 Mar 20 Apr - 31 May 02 Tuesday 12:00 - 13:00 C1 Lecture Theatre (18/2-17/3)- (24/3, 21/4)Online Delivery (28/4-26/5) 17 Feb - 29 Mar 20 Apr - 31 May Lecture C 01 Wednesday 08:00 - 09:00 C1 Lecture Theatre (19/2-18/3)- (25/3, 22/4)Online Delivery (29/4-27/5) 17 Feb - 29 Mar 20 Apr - 31 May 02 Wednesday 12:00 - 13:00 A1 Lecture Theatre (19/2-18/3)- (25/3, 22/4)Online Delivery (29/4-27/5) 17 Feb - 29 Mar 20 Apr - 31 May Lecture D 01 Thursday 10:00 - 11:00 C1 Lecture Theatre (20/2-19/3)- (23/4-28/5) 17 Feb - 22 Mar 20 Apr - 31 May 02 Thursday 14:00 - 15:00 C1 Lecture Theatre (20/2-19/3)- (23/4-28/5) 17 Feb - 22 Mar 20 Apr - 31 May Tutorial A 01 Wednesday 13:00 - 14:00 17 Feb - 29 Mar 20 Apr - 31 May 02 Thursday 09:00 - 10:00 17 Feb - 22 Mar 20 Apr - 31 May 03 Friday 12:00 - 13:00 17 Feb - 22 Mar 20 Apr - 31 May 05 Friday 15:00 - 16:00 17 Feb - 22 Mar 20 Apr - 31 May 06 Tuesday 14:00 - 15:00 17 Feb - 29 Mar 20 Apr - 31 May 08 Monday 09:00 - 10:00 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May 09 Friday 13:00 - 14:00 17 Feb - 22 Mar 20 Apr - 31 May 10 Monday 13:00 - 14:00 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May 12 Wednesday 11:00 - 12:00 17 Feb - 29 Mar 20 Apr - 31 May 13 Thursday 16:00 - 17:00 17 Feb - 22 Mar 20 Apr - 31 May 14 Thursday 11:00 - 12:00 17 Feb - 22 Mar 20 Apr - 31 May 15 Tuesday 16:00 - 17:00 17 Feb - 29 Mar 20 Apr - 31 May 16 Thursday 13:00 - 14:00 17 Feb - 22 Mar 20 Apr - 31 May 17 Tuesday 13:00 - 14:00 17 Feb - 29 Mar 20 Apr - 31 May 18 Monday 15:00 - 16:00 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May 20 Wednesday 14:00 - 15:00 17 Feb - 29 Mar 20 Apr - 31 May 22 Monday 10:00 - 11:00 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May 23 Thursday 10:00 - 11:00 17 Feb - 22 Mar 20 Apr - 31 May 24 Monday 16:00 - 17:00 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May 25 Monday 13:00 - 14:00 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May 26 Wednesday 15:00 - 16:00 17 Feb - 29 Mar 20 Apr - 31 May 27 Friday 14:00 - 15:00 17 Feb - 22 Mar 20 Apr - 31 May 28 Friday 10:00 - 11:00 17 Feb - 22 Mar 20 Apr - 31 May 29 Tuesday 10:00 - 11:00 17 Feb - 29 Mar 20 Apr - 31 May 30 Tuesday 15:00 - 16:00 17 Feb - 29 Mar 20 Apr - 31 May 31 Tuesday 09:00 - 10:00 17 Feb - 29 Mar 20 Apr - 31 May 32 Wednesday 13:00 - 14:00 17 Feb - 29 Mar 20 Apr - 31 May 33 Friday 09:00 - 10:00 17 Feb - 22 Mar 20 Apr - 31 May 34 Monday 11:00 - 12:00 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May 35 Thursday 14:00 - 15:00 17 Feb - 22 Mar 20 Apr - 26 Apr 4 May - 31 May 36 Wednesday 10:00 - 11:00 17 Feb - 29 Mar 20 Apr - 31 May 37 Monday 12:00 - 13:00 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May

## Examination and Formal Tests

Activity Day Time Location Test A 01-P1 Wednesday 12:00 - 00:00 27 Apr - 3 May 01-P2 Thursday 07:00 - 12:00 27 Apr - 3 May

## Course Coordinator

For further information see Mathematics and Statistics Head of Department

## Assessment

To pass the course, there is a minimum mark required in the Final Examination of 40%, as well as achieving 50% or more in total across all the assessments.

## Textbooks / Resources

•“Advanced Engineering Mathematics” by Erwin Kreyszig. (This text also covers the statistics material.)
•“Advanced Engineering Mathematics” by Zill and Wright.
•“Advanced Engineering Mathematics” by Zill and Cullen.

## Indicative Fees

Domestic fee \$975.00

International fee \$5,500.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

## All EMTH210 Occurrences

• EMTH210-20S1 (C) Semester One 2020